LR Question 19 Explanation
QUESTION TEXT: In West Calverton, most pet stores sell exotic birds…
QUESTION TYPE: Must Be True
FACTS:
- Pet store (Most) ➞ has birds
- Has birds (Most) ➞ Has fish
- Fish and
Birds➞ Gerbils - Contrapositive:
Gerbils➞ NOT(Fish andBirds)
ANALYSIS: First, you can’t combine “most” statements with anything. You can only combine “most” statements with the sufficient condition of a conditional statement.
Second, let’s talk about contrapositives. Normally, you would draw a contrapositive by negating both statements, and changing “and” to “or”, like this:
Gerbils ➞ Fish or Birds
You probably drew that, but still struggled. The diagramming method above is just a trick to get you to the right place. But it’s better to know what a contrapositive really is.
Contrapositives are really just “not that”, whatever that is. The negation of something is just “not that thing”. This gets complicated with compound conditions (e.g. this AND that). There are four possibilities with any compound statement. Let’s use tropical fish and exotic birds as an example:
- Fish and birds
Fishand birds- Fish and
birds Fishandbirds
The sufficient condition in the stimulus is the third one. So the contrapositive is “not the third one”. So numbers 1, 2 and 4 are all included in the contrapositive.
“NOT(Fish and Birds)” capture this idea better than “Fish or Birds”. Both statements actually mean “any of 1, 2 or 4”, but the first one is much clearer. And the correct answer, D, is phrased in the form of “NOT(Fish and Birds)”.
___________
- We only know that independently owned pet stores don’t sell gerbils. This answer says “most”. The fact about gerbils doesn’t connect with any “most” statements.
- We only know that no independently owned pet stores sell gerbils. This answer talks about all pet stores. The bird and fish part is wrong too: it should have said “no pet stores….sell tropical fish but not exotic birds”. That’s what we can conclude about a pet store that doesn’t sell gerbils.
- We don’t even know if any independently owned pet stores do sell gerbils. The question gives us a sufficient condition for a store to sell gerbils, but it doesn’t tell us whether any pet stores do meet that sufficient condition.
- CORRECT. This is the contrapositive of the conditional statement from the stimulus. If a pet store “sells tropical fish but not exotic birds” then it sell gerbils.
So if a pet store doesn’t sell gerbils, then it doesn’t “sell tropical fish and not exotic birds”.
Note: And = But
See the analysis section above for more detail. - We have no idea. We know that independent pet stores don’t sell gerbils. That just means they can’t “sell tropical fish but not exotic birds”.
As long as they don’t do that, they could sell:
1. Tropical fish and exotic birds
2. No tropical fish and no exotic birds
3. No tropical fish, and exotic birds. This answer is too restricted. It excludes the third possibility.
Recap: The question begins with “In West Calverton, most pet stores”. It is a Must be True question. To practice more Must be True questions, have a look at the LSAT Questions by Type page.
More Resources for Must Be True Questions
- Conditional Reasoning Article: Learn about conditional statements on the LSAT.
- LR Diagrams Guide: Learn how to draw LR diagrams.
- Intro to Conditional Reasoning: This intro course lesson covers conditional reasoning basics.
- Intro Course lesson: This intro course lesson covers Must Be True questions.
- Mastery Seminar lesson: This LR Mastery seminar lesson covers must be true questions.
Shouldn’t #4. Be NOT(Fish or -Birds-)? I thought when using the contrapositive, “and” becomes “or”
Good question. This is a special case, or rather, it’s another way of phrasing the same thing. For example, suppose I say: if you have a pet, you have a Cat or a dog. Pet –> Cat or Dog
You can negate the second half in two ways:
* NOT (Cat or Dog) = It is not true that you have a cat or a dog
* ~Cat and ~Dog = You have no cat and no dog.
Both versions mean the same thing, they’re just expressed differently. Basically you’re saying “that necessary condition is not true”. I wrote it the way I did because that’s how the answer expresses it. But I agree it is potentially confusing – that’s what makes this a hard question!
If you want to get way to technical on this point, this concept is called De Morgan’s Law. I don’t pretend to fully understand it.
Note: This is an old comment but I wanted to clarify the point.
In blind review, I seem to have reached the correct answer without taking the contrapositive. Maybe I am misunderstanding my own work…
Fish + ~Birds –> Gerbils –> ~Independent
Answer choice D: I translated this to Fish + ~Birds –> ~Independent, which matches my initial diagram less Gerbils.
I don’t see independent stores anywhere in your upfront diagraming but it is what allowed me to answer this question. If I am mistaken please let me know. Thanks!
Yes, your line of reasoning and diagrams are correct. Students often (also correctly) diagram the last line of the stimulus as: Independent –> ~Gerbils. This is because statements of the form “No A’s are B’s” are usually more easily expressed as A –> ~B. However, B –> ~A is also correct; it’s just the contrapositive.
So, by diagramming it the way you did, you were able to skip taking the contrapositive, make the conditional chain, and get to answer choice (D) more easily.